J Control Autom Electr Syst (2015) 26:46–56 DOI 10.1007/s40313-014-0156-0 An Alternative Way to Model Switches and Circuit Breakers to Directly Determine Short-Circuit Currents Flowing Through Them Isabel S. Duarte · Thelma S. P. Fernandes · Elizete. M. Lourenço Received: 31 March 2014 / Revised: 22 July 2014 / Accepted: 18 September 2014 / Published online: 21 October 2014 © Brazilian Society for Automatics–SBA 2014 Abstract This paper proposes an extension of the tradi- tional mathematical formulation of short-circuit analysis in order to make it able to process networks modeled at bus- section level. Differently from the existing methodology for calculating short-circuit currents, which is based on the con- ventional bus-branch network model, the proposed approach processes networks modeled at the physical level, allow- ing the direct determination of short-circuit currents through closed-circuit breakers. For this purpose, the current through circuit breakers is included in the problem as a new state variable. Besides, information regarding the closed status position of circuit breakers is taken into account as addi- tional linear equations, producing a non-redundant set of algebraic equations. The proposed approach provides an effi- cient tool for directly determining the short-circuit current flowing through circuit breakers into a selected substation of the network, avoiding unreliable artifices and tedious post- processing procedures required by the existing methodology, which is based on the bus/branch model. Simulations con- ducted on a five-bus test system and a 291-bus test system are used to illustrate the proposed methodology. Keywords Bus-section level modeling · Circuit breakers · Short-circuit current 1 Introduction When an electric network is under a fault situation, the operating conditions change, altering the electrical quan- tities, which can cause violations of the equipment’s lim- I. S. Duarte · T. S. P. Fernandes (B) · E. M. Lourenço Department of Electrical Engineering, Federal University of Paraná, Curitiba, PR 81531-990, Brazil e-mail: thelma@eletrica.ufpr.br its. Besides, the constant growth of global demand calls for continuous adaptations of electrical power systems, which require, for example, a continuous analysis of short-circuit values at several points of the power network in order to plan, coordinate protection, and estimate the consequences of a wide range of faults and thus make possible corrective measures viable. These measures include installation, adjust- ment, and/or coordination of devices that allow interruption of damaged circuits and ensure that all network components can support the effects. Thus, short-circuit studies allow the dimensioning of transmission lines in relation to their thermal limit, the defi- nition of circuit-breaker interruption capacity, dimensioning of current transformers in terms of saturation, establishment of protection relay adjustments, analysis of over and under voltages, knowledge of relay action time, and the study of the dynamic stability of the power system. Furthermore, as short-circuit current values are almost non-dependent of loads and predominantly dependent on the system capacity, they should be recalculated whenever the generating capacity increases or the system changes. Consequently, constant supervision of equipment capacity must be performed, such as the calculations of fault currents flowing through the circuit breakers that are inside the sub- stations. Despite the need to model each circuit breaker indi- vidually, there are some impediments to doing so by the usual methodologies. For example, the practice of model- ing a circuit breaker with small impedances (adopting an arbitrary value for the branch series impedance) causes ill- conditioning of the ˙ Y bus matrix. In addition, this impedance should be small enough to not affect the accuracy of results and big enough to yield a well-conditioned ˙ Y bus matrix. So, the usual methodologies, such as Nodal Analysis (Stevenson 1974; Bergen 2000), used to calculate short- 123